# Seminars & Events for PACM/Applied Mathematics Colloquium

##### Curvature suppresses the Rayleigh-Taylor instability

PLEASE CLICK ON COLLOQUIUM TITLE FOR EACH COMPLETE ABSTRACT. Naima Hammoud's abstract: Thin films on curved surfaces are widely observed in coating and painting processes and wetting problems.

Haoshu Tian's abstract: The default of one bank can cause other banks to default through two channels: financial contagion in the inter-bank liability network and fire sale in the asset selling market. When the defaulted bank cannot fully pay its debt, the loss is transmitted to other banks.

##### Coarsening to Chaos-Stabilized Fronts in Pattern Formation with Galilean Invariance

The presence of continuous symmetries, or coupling with a large-scale mode or mean flow, can strongly influence the dynamics of pattern-forming systems. After reviewing some aspects of pattern formation and spatiotemporal chaos in one-dimensional Kuramoto-Sivashinsky-type equations, I will focus on a 6th-order analogue, the Nikolaevskiy PDE, a model for short-wave pattern formation with Galilean invariance displaying spatiotemporal chaos with strong scale separation. I will discuss this PDE and its relation with the corresponding leading-order amplitude equations for the coupled long-wave and pattern modes. These equations, derived by Matthews and Cox, display unexpectedly rich, strongly system-size-dependent dynamics; I will describe their long-time behavior, which has a single stable Burgers-like viscous shock coexisting with a ch

##### Graph limits and planted partitions from the perspective of probability and statistics

**SPECIAL PACM COLLOQUIUM: **The theory of dense graph limits has emerged as a well established tool in modern combinatorics, with close connections to applied probability and ergodic theory. In this talk we answer a probabilist's question first posed by Aldous and subsequently pursued by Kallenberg: given a single observation of a large network generated by a graph limit function (graphon) subject to bond percolation, how much information can we recover about the data-generating model? Results come by way of blockmodels, which generalize the ideas underlying the planted partition problem in theoretical computer science, as well as the community detection problem in applications of network clustering to the social and biological sciences.